The next result studies an objective used in the classic work of [1]}. We evaluate performance at a random time \(\tau \)  at which the decision-maker decides to stop collecting measurements. We take the total expected cost incurred by running an adaptive experiment, when the true state of nature is \(\theta _0\) , to be
\(\mathbb {E}\left[c \tau + \Delta _{\tau } \mid \theta =\theta _0\right],\) 
